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\section*{December 11, 1996 Addendum to: Nakauchi, N.,
{\em A remark on $\infty$-harmonic functions on Riemannian manifolds},
Electr. J. Diff. Eqns. Vol. 1995(1995), No. 07, pp. 1--10.}
In this article, Theorem 1 follows from general properties
of the Riemannian curvature tensor, and Corollary 1 is incorrect.
The Bochner formula does not seem to work in this situation.
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Lemma 1 can be used in proving the following Liouville theorem
for ${\rm C}^{3}$-solutions.
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\noindent{\bf Theorem A.} {\it Let $M$ be a complete noncompact
Riemannian manifold of nonnegative (sectional) curvature.
Let $u$ be a bounded $\infty$-harmonic function of
${\rm C}^{3}$-class on $M$.
Then $u$ is a constant function. }
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The curvature assumption in Theorem A is necessary only for applying the
Hessian comparison theorem in the proof (Here we use the operator
${\rm Q}^{ij} = g^{ip}g^{jq}\nabla_{p}\nabla_{q}$).
Theorem A also follows from arguments in [Cheng, S.Y.,
{\em Liouville theorem for harmonic maps},
Proc. Symp. Pure Math. 36(1980), 147-151]. See also the article
[Hong, N.C., {\it Liouville theorems for exponentially harmonic
functions on Riemannian manifolds}, Manuscripta Math. 77(1992), 41-46].
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Sincerely yours,
Nobumitsu Nakauchi
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